higgins - confined steel brace for earthquake resistant design

In the United States, there is a shift toward performance-based design of structures and increased demand for

higher structural performance during earthquakes. Buildingowners are increasingly interested in immediate occupancyfollowing large earthquakes and want to mitigate economiclosses due to structural damage during a seismic event. Onemethod for protecting structures and achieving higher per-formance levels is the application of passive energy dissi-paters. Viscous, viscoelastic, and metallic dampers arepassive devices currently used to increase the performancelevel of structures during seismic events. While viscous andviscoelastic dampers are becoming more common, applica-tion of metallic dampers has recently begun to increase inthe U.S.

Metallic dampers rely on the hysteretic damping capacityof the metal component of the device and the post-yieldproperties of the metallic elements to provide the designlevel of ductility and energy dissipation. The metallicdamper system utilizes the inelastic deformation allowanceof the Uniform Building Code (ICBO, 1997) by providingelements designed to dissipate the input seismic energythrough controlled cyclic inelastic deformations.

One such metallic damper, a tension-compression yield-ing brace or buckling-restrained brace (BRB) termed theUnbonded Brace™ (UBB) has been developed by NipponSteel of Japan (Aiken, Clark, Tajirian, Kasai, Kimura, andKo, 2000; Black, Makris, and Aiken, 2002; Wantanabe,1992; Wantanabe, Hitomi, Saeki, Wada, and Jujimoto,1988). Other BRBs have been developed and tested in theU.S. (Merritt, Uang, and Benzoni, 2003a; Merritt, Uang,

and Benzoni, 2003b; Merritt, Uang, and Benzoni, 2003c).Japanese practice typically incorporates UBBs as separatepassive energy dissipation elements in moment resistingframes. In this application the UBB devices act as metallicdampers. U.S. practice has been to use buckling-restrainedbraces to replace conventional brace members in bracedframe construction. In this application the buckling-restrained brace serves as a ductile brace with improvedtension/compression characteristics as compared with con-ventional bracing members. The UBB relies upon a struc-tural tube filled with mortar that confines a steel yieldingcore. A debonding agent is applied between the concreteand steel allowing space for Poisson’s effect and reducingshear stress transfer between the steel yielding core, mortar,and confining tube. The mortar provides buckling resist-ance that allows the steel core to yield in compression aswell as in tension, thereby permitting stable and symmetrichysteretic energy dissipation capacity under fully reversedcyclic loading. To ensure that the damper does not buckle inthe first mode, the UBB must satisfy the following condition:

where E = Young’s Modulus I = moment of inertia of the outer confining tubeL = brace length, taken as work-point to work-pointα = global buckling factor of safetyP = design axial load including the effects of strain

hardening (Wantanabe, 1992) When the conditions of this equation are met, the exter-

nal structural tube will provide the necessary global buck-ling resistance and enable the steel core to yield incompression instead of global brace buckling in first mode.Testing and analysis conducted to assess the performance ofBRBs indicated the device provides stable, reasonably sym-metric hysteretic energy dissipation of the input cyclic load-ing (Aiken and others, 2000; Black and others, 2002;Tremblay, Degrange, and Blouin, 1999; Wantanabe, 1992;Wantanabe and others, 1988).

ENGINEERING JOURNAL / FOURTH QUARTER / 2004 / 187

Confined Steel Brace forEarthquake Resistant Design

CHRISTOPHER C. HIGGINS and JAMES D. NEWELL

Christopher C. Higgins is assistant professor, department ofcivil, construction and environmental engineering, OregonState University, Corvallis, OR.

James D. Newell is graduate student researcher, depart-ment of structural engineering, University of California, SanDiego, La Jolla, CA, and formerly graduate research assis-tant, department of civil, construction and environmentalengineering, Oregon State University, Corvallis, OR.

2

2

EI PL

π α≥ (1)

Buckling-restrained braced frames (BRBF) with UBBshave seen over 200 Japanese applications since 1987 (Blackand others, 2002) and are gaining increased acceptance as aseismic force resisting system (SFRS) by the U.S. structuralengineering community. BRBFs have been used in about 30U.S. projects to date, including both new and retrofit con-struction. Most applications have used imported NipponSteel UBBs from Japan. Currently, no adopted U.S. build-ing code provisions exist for BRBF design. Recommendedprovisions have been developed by a joint American Insti-tute of Steel Construction/Structural Engineers Associationof California (AISC/SEAOC) committee, and this work hasbeen incorporated into the 2003 NEHRP RecommendedProvisions for Seismic Regulation of New Buildings andOther Structures (FEMA, 2003) and will be incorporatedinto the 2005 AISC Seismic Provisions for Structural SteelBuildings.

This paper addresses an economical, low-yield forcealternative form of BRB in which the mortar of the UBB isreplaced with confined non-cohesive material. This non-cohesive material provides buckling resistance of the core,enabling the device to yield in compression and in tension.Confined Yielding Braces (CYBs) provide benefits includ-ing economical use of standard materials, for example,ASTM A36 steel bar stock for the yielding core and ASTMA53A steel pipe for the confining tube. Further, this newdevice offers simplified connection design and detailing,opens the market for non-proprietary U.S. fabrication ofCYBs using no patented technologies, offers applicabilityto a wider range of building structures as the brace yieldforce levels under investigation are lower than are currentlyavailable, and simplified design of the damper devicebecause no debonding layer is required.

EXPERIMENTAL PROGRAM

Test Specimens

Small scale experimental CYB tests were carried out atClarkson University (Higgins and Newell, 2001; Higginsand Newell, 2002). Test results indicated relatively stableand symmetric hysteretic damping with a reduced scaledevice. The current testing program was therefore under-taken to characterize large-scale CYB performance andestablish design guidelines for future application of CYBsas a SFRS in structures.

In this research, two different yield force levels wereinvestigated: 125 kip (556 kN) and a 50 kip (222 kN) yieldforce levels. These yield force levels correspond to braceseismic force demand in typical one to three story buildingsand would represent a reduced scale device for larger struc-tures. A dogbone and perforated yielding core configurationwere tested at each force level. The CYB configurations,illustrated in Figure 1, consist of a steel yielding core ele-ment within a steel pipe filled with a confined non-cohesivematerial. The non-cohesive material takes the place of themortar used in the UBB in providing lateral stability to theyielding core. Specimen cross-sections are shown in Figure2. A constant confining material volume was maintainedwith steel end caps and 1/2 in. (12.70 mm) diameter A193B-7 high-strength threaded rod. Threaded rods were ten-sioned to 5 kips (22.2 kN) each, as measured by bolt loadcells, to provide confining pressure. The use of threadedrods and a removable end cap also facilitated the removal ofconfining material for post-event yielding core inspectionand repair/replacement while reusing major portions of thedevice.

188 / ENGINEERING JOURNAL / FOURTH QUARTER / 2004

Fig. 1. CYB configurations.

To determine realistic brace geometry for testing, typicalframe member sizes and dimensions were considered.Columns were assumed to be W14 sections and beams wereassumed to be W21 sections. A full-scale specimen yieldingcore length of 16 ft (4.88 m) was selected for a single diag-onal brace in a typical bay with column-to-column center-line spacing of 15 ft (4.57 m), beam-to-beam centerlinespacing of 13 ft (3.96 m) and considering the gusset platebeam-to-column-to-brace connection, as illustrated inFigure 3.

The yielding core reduced cross-sectional area was cal-culated based on the desired yield force and material prop-erties determined from tension coupon testing. Thedogbone configuration, with a reduced width yielding coresegment and unreduced width connection/transition region,is typical of current BRBs. The perforated configuration hasthe potential for greater design variation in the yield forceand stiffness of the device by varying the geometric proper-ties, and was also investigated. The legs of different perfo-rations could be fabricated to different lengths,


Mild Steel (A36) Yielding Brace

Fig. 2. CYB cross-sections.

Fig. 3. Frame geometry with CYB.

A36 Steel Yielding CoreDogbone Reduced Section(1-1/4 in. x 1-15/16 in.)

A36 Steel Yielding CoreDogbone Reduced Section(3/4 in. x 1-11/16 in.)

cross-sectional areas or tapered allowing for tailoring ofdevice performance. Fabrication costs for the dogbone andperforated configurations were equal for a given yield forceCYB.

Specimens were identified by yield force level, yieldingcore configuration, and specimen identification number.For example, 125DB-1 was a 125 kip (556 kN) yield force,dogbone configuration, and specimen identification number1. 50P-2 was a 50 kip (222 kN) yield force, perforated con-figuration, and specimen identification number 2.

The 125 kip yield force dampers consisted of 11/4 in.(31.75 mm) by 6 in. (152.40 mm) A36 steel bar stock witha yield stress (Fy) of 51.8 ksi (357.2 MPa) and an ultimatestress (Fu) of 72.1 ksi (497.1 MPa), based on tensioncoupon testing. The reduced cross-sectional area of the125DB specimen was 2.422 in.2 (1562.6 mm2), and thereduced cross-sectional area of each leg of the 125P speci-men was 1.211 in.2 (781.3 mm2), resulting in an area forboth legs equivalent to that of the dogbone specimen.Length of individual perforation legs was 11 in. (279.40mm) with a 2.3 factor of safety against buckling assumingpinned ends at the ends of the legs. Yielding core geometryfor all specimens is shown in Figure 4. Two 3/4 in. (25.4

mm) by 6 in. (152.40 mm) A36 splice plates were used toconnect the yielding core to the reaction system. The con-fining tube for the 125 kip (556 kN) yield force specimenswas an 8 in. (203.20 mm) extra heavy steel pipe (A53A)with a factor of safety against global buckling of 2.7 assum-ing pin-ended connections for the brace, work-point towork-point on the brace length, and considering the com-pressive stress of the yielding core including strain harden-ing.

The 50 kip (222 kN) yield force dampers consisted of3/4 in. (19.05 mm) by 41/2 in. (114.30 mm) A36 steel barstock with a yield stress (Fy) of 39.5 ksi (272.4 MPa) and anultimate stress (Fu) of 63.6 ksi (438.5 MPa). The reducedcross-sectional area of the 50DB specimen was 1.266 in.2(816.7 mm2), and the reduced cross-sectional area of eachleg of the 50P specimen was 0.633 in.2 (408.4 mm2) pro-viding an area of both legs equivalent to that of the dogbonespecimen. Length of individual perforation legs was 9 in. witha 2.4 factor of safety against buckling assuming pinnedends for individual legs. Yielding core geometry is shown inFigure 4. Two 1 in. (25.4 mm) by 6 in. (152.40 mm) A36splice plates were used to connect the yielding core to thereaction system. The confining tube for the 50 kip (222 kN)


Fig. 4. Yielding core geometries.

yield force specimens was a 6 in. (152.40 mm) extra heavysteel pipe (A53A) with a factor of safety against buckling of2.3 using previous assumptions.

Yielding core elastic stiffness and yield displacement val-ues are summarized in Table 1 and take into account theunreduced sections of the yielding core that remain elasticafter the reduced sections have yielded up to the first line ofbolts.

Connections for both yield force levels were detailed asslip-critical bolted connections with Class A slip surfacesand fully-tensioned ASTM A490 high-strength structuralbolts designed per the 1993 Load and Resistance FactorDesign Specification for Structural Steel Buildings (AISC,1993). Six (6) 1-in.-diameter (25.40 mm) A490 bolts wereused for the 125 kip (556 kN) yield force specimens andfive (5) 3/4-in.-diameter (19 mm) A490 bolts were used for the50 kip (222 kN) yield force specimens. Connections weredesigned to resist the ultimate strength (Fu) of the steelyielding core as determined from tension coupon testingand also taking into account the compressive overstrengthfactor of 1.1 typical of previously tested BRBs (Aiken andothers, 2000). The net section of the connection wasdesigned to remain elastic at a load equal to the yieldingcore ultimate tensile strength. Washers were used underboth the head of the bolt and nut per RCSC Specification forStructural Joints (RCSC, 1994) for steel with a nominalyield stress less than 40 ksi (275.8 MPa).

Structural Test Matrix

Fourteen large-scale CYBs were tested to characterizedevice performance and investigate the influence of variousparameters on behavior as shown in the test matrix, Table 2.The performance of different confining materials wasinvestigated using the 125 DB specimens. Four differentreadily available aggregates were used as confining mate-rial: sand, pea gravel (1/4 in. (6.35 mm) minus gravel), 3/4 in.

(19.05 mm) to #4 (4.75 mm) gravel, and 3/4 in. (19.05 mm)minus gravel (which consisted of equal parts of the above).Pea gravel was used as the confining material for all otherspecimens. Different configurations of perforation blocking(Figure 5) were tested with the 125P specimens to optimizeperformance and minimize lower modes of buckling forindividual legs. A decreasing amplitude displacement his-tory was compared to the typical increasing amplitude dis-placement protocol with the 50DB specimens. CYBperformance when subjected to a random displacement his-tory was evaluated with the 50P specimens with perforationblocking as shown in Figure 5.

Specimen Fabrication

The dogbone and perforated configuration yielding coreswere fabricated using abrasive water jet cutting techniques.A 50,000 psi (344.75 MPa) water and garnet abrasive cut-ting stream was CNC controlled to cut the required config-urations. Testing of both water jet and traditionallymachined tension coupons did not indicate a change in thestress-strain behavior from the water jet cutting process forthe 11/4 in. (31.75 mm) A36 steel bar stock used for the 125kip (556 kN) yielding cores.

The weight of confining material placed in the tube wascalculated to achieve approximately 95 percent relativedensity. Actual confining material volumes, weights, anddensities are given in Table 3. The tube was filled with con-fining material in a vertical orientation with the yieldingcore maintained in proper alignment. Confining materialwas placed in approximately 30 lb (0.13 kN) lifts and com-pacted internally with a pencil vibrator and/or externallywith a 5 lb (0.02 kN) dead blow hammer on the outside ofthe confining tube. Method of compaction is included inTable 3. Sheet metal and spray foam crush-zones 6 in.(152.40 mm) in length were added to the dogbone yieldingcores in the transition zone from reduced to unreduced cross


Table 1. Yielding Core Properties

Specimen

(ksi) (MPa) (ksi) (MPa) (in.2) (mm

2) (kip) (kN) (in.) (mm) (kip/in.) (kN/mm)

(1)

125DB 51.8 357.2 72.1 497.1 2.422 1562.6 125 556 0.278 7.06 451 79.0

125P 51.8 357.2 72.1 497.1 2.422 1562.6 125 556 0.216 5.49 581 101.7

50DB 39.5 272.4 63.6 438.5 1.266 816.8 50 222 0.222 5.64 225 39.4

50P 39.5 272.4 63.6 438.5 1.266 816.8 50 222 0.174 4.42 287 50.3

Kby

Area of

Reduced

Cross-Section

Yield

Stress

F y

Ultimate

Stress

F u

(2) (3) (4)

Local Brace

Stiffness

(7)(6)(5)

Yield

Displacement

Yield

Force

P y


Specimen Parameter

(1) (2)

125DBa-1 Pea Gravel

125DB-2 Pea Gravel (Pencil Vibrator)

125DB-3 Sand

125DB-4 3/4" - #4 Gravel

125DB-5 3/4" - minus Gravel

125Pb-1 All perforations spray foamed

125P-2 First perforation @ each end completely blocked,

remaining perforations with spray foamed radius

125P-3 First 2 perforations @ each end completely blocked,

remaining perforations with spray foamed radius


remaining perforations blocked with knockout minus

2 in. length (with cut in middle of knockout)


remaining perforations blocked with plate minus

2 in. length, minus 1/2 in. width

50DB-1 Increasing amplitude displacement protocol

50DB-2 Reverse displacement protocol from 2.0 bm

50P-1 Increasing amplitude displacement protocol

50P-2 Random displacement history

aDB - Dogbone configuration

bP - Perforated configuration

Table 2. Test Matrix

Table 3 Confining Material Properties

Specimen Confining MaterialCompaction

Method

(lb) (kN) (ft3) (m

3) (lb/ft

3) (kN/m

3)

(1) (2) (3)

125DBa-1 Pea Gravel DBH

c412.00 1.83 3.88 0.1099 106.19 16.68

125DB-2 Pea Gravel DBH/PVd

438.50 1.95 3.85 0.1090 113.90 17.89

125DB-3 Sand DBH 382.50 1.70 3.86 0.1093 99.09 15.56

125DB-4 3/4" - #4 Gravel DBH 400.00 1.78 3.88 0.1099 103.09 16.19

125DB-5 3/4" - minus Gravel DBH 466.75 2.08 3.88 0.1099 120.30 18.89

125Pb-1 Pea Gravel DBH 361.75 1.61 3.46 0.0980 104.55 16.42

125P-2 Pea Gravel DBH 390.25 1.74 3.66 0.1037 106.63 16.75125P-3 Pea Gravel DBH 375.75 1.67 3.59 0.1017 104.67 16.44125P-4 Pea Gravel DBH 356.00 1.58 3.46 0.0980 102.89 16.16125P-5 Pea Gravel DBH/PV 387.50 1.72 3.44 0.0974 112.65 17.69

50DB-1 Pea Gravel DBH/PV 265.75 1.18 2.28 0.0646 116.56 18.31

50DB-2 Pea Gravel DBH/PV 268.25 1.19 2.28 0.0646 117.65 18.48

50P-1 Pea Gravel DBH/PV 236.00 1.05 2.10 0.0595 112.38 17.65

50P-2 Pea Gravel DBH/PV 231.25 1.03 2.10 0.0595 110.12 17.30



cDBH - Dead blow hammer

dPV - Pencil vibrator

Weight of

Confining Material

(4)

Confining Material

Density

(6)(5)

Volume of

Voids

Table 3. Confining Material Properties

section to minimize compressive stiffening from the shoul-ders of the dogbone shaped yielding core bearing on theconfining material. Perforated yielding cores were encasedin sheet metal to maintain alignment of blocking materialwithin individual perforations.

Structural Testing Setup

Specimens were tested in a horizontal configuration, Figure 6,with a structural steel reaction system at each end attached

to the laboratory strong floor. Roller supports were pro-vided at approximate third points of the confining tube toprotect the test setup from any overall damper instability.The rollers provided negligible resistance to tube move-ment in the brace axial direction but prevented any exces-sive deformation in the transverse directions. Load wasapplied at a rate of 1.33 in./min (33.78 mm/min) with a 500kip (2,224 kN) capacity servo-controlled hydraulic actuator.Specimen yielding core axial deformation was used as thefeedback sensor for displacement control of the servo-


Fig. 5. CYB blocking configurations used with perforated specimens.

CYB Specimen

Fig. 6. Experimental setup.

hydraulic system. Instrumentation consisted of strain gages,displacement transducers, and a load cell in series with thespecimen. Strain gages on the steel yielding cores and con-fining tube were used to measure axial strains and deter-mine if bending was occurring within the elastic range ofthe gages. Two displacement sensors (string potentiome-ters) were used to measure overall yielding core deforma-tion. Displacement values from these two sensors wereaveraged to remove any bending component due to braceend-rotation outside of the confining tube. Instrumentationlayout for all sensors is detailed in Newell (2003). A PC-based data acquisition system was used to acquire data at acontinuous rate of 5 Hz during testing.

Increasing Amplitude Displacement Protocol

The displacement protocol (Figure 7) was based on theguidelines of ATC 24 (ATC, 1992) and the AISC/SEAOCRecommended Buckling-Restrained Brace Frame Provi-sions (AISC/SEAOC, 2001). Increasing amplitude fullyreversed cyclic axial displacement was applied until failure.Two cycles each were applied at 0.25 ∆by, 0.50 ∆by, and 0.75∆by, where ∆by equaled the yield displacement of the steelcore. Six cycles at ∆by were then applied. The remainingprotocol was based on the design story drift of 1 percent(∆bm, 1.19 in. (30.23 mm) local brace displacement) on theframe geometry shown in Figure 3. Four cycles each wereapplied at deformation levels corresponding to 0.5 ∆bm, 1.0∆bm, and 1.5 ∆bm. Two cycles were applied at 2.0 ∆bm andhigher deformation levels incremented by 0.5 ∆bm to failure.Design story drift of 1 percent corresponded to the mini-mum recommended value for determination of ∆bm(AISC/SEAOC, 2001) and was selected to represent a mod-erate earthquake demand for the initial experimental evalu-

ation of large-scale CYB devices. The loading protocoldeveloped for this testing also applied two cycles at 2.0 ∆bmand higher deformation levels incremented by 0.5 ∆bm tofailure where the AISC/SEAOC protocol would return to1.0 ∆bm until a cumulative ductility value of 140 ∆by wasachieved. CYB specimens were therefore subjected todeformation demands greater than that resulting from theAISC/SEAOC loading protocol based on 1 percent storydrift.

Random Displacement History Development

Specimen 50P-2 was subjected to multiple iterations of arandom displacement history derived from nonlineardynamic time-history analysis of a three-story BRBF build-ing. The building modeled in this analysis is based on thework of Sabelli (2000) and the SAC model building designcriteria. The SFRS consisted of eight BRBFs with four ineach orthogonal direction. The building was designed for asite in metropolitan Los Angeles according to the 1997NEHRP Recommended Provisions for Seismic Regulationof New Buildings and Other Structures (FEMA, 1997) andthe 1997 Uniform Building Code (ICBO, 1997).

For analysis, one BRBF was modeled with an additionalsingle column representing the secondary P-∆ load affectattributed to the BRBF. The horizontal stiffness contribu-tion of this equivalent gravity framing column was neg-lected as is standard design practice. The frame model isshown in Figure 8 and member properties reported inTable 4.

Nonlinear dynamic time history analysis was conductedusing the computer program PC-ANSR (Maison, 1992).Frame members were modeled as nonlinear beam-columnelements. Beams were considered inextensible. Nodal dis-


Fig. 8. Three-story BRBF model.

Time (min.)

Dis

plac

emen

t (in

.)

0 15 30 45 60 75 90 105 120-3

-2

-1

0

1

2

3

Fig. 7. Increasing amplitude displacement protocol imposed on most test specimens.

placements within a story were set to be equivalent. Con-nections with gusset plates for brace attachment were mod-eled as rigid. The roof beam/column connections where nobraces framed in were considered pinned (simple shear tab).All framing members were ASTM A992 steel, with a strainhardening modulus 5 percent that of Young’s Modulus.Braces were modeled as nonlinear truss elements. ASTMA36 steel was assumed for the braces. The compressiveyield stress was modeled as 110 percent of the tensile yieldstress, based on previous buckling-restrained brace testresults (Aiken and others, 2000). Brace cross-sectional areawas calculated from the brace yield force given by Sabelli(2000) and a nominal yield stress of 36 ksi. An equivalentYoung’s Modulus was then calculated from this area andthe required horizontal brace stiffness. A post-yield slope of1 percent of the brace elastic stiffness was used, as deter-mined from published UBB experimental testing load-dis-placement response (Aiken and others, 2000). Equivalentviscous damping of 5 percent was assumed for the structureper standard practice in the seismic design of steel struc-tures and was applied as mass and initial stiffness propor-tional damping factors.

Ground motions considered (LA01-LA20) were devel-oped for the SAC steel project (Woodward-Clyde FederalServices, 1997). The 20 earthquake records used are for asite in Los Angeles with a 10 percent probability of excee-dence in 50 years. Nonlinear dynamic time history analysiswas completed for the LA series earthquakes and the resultsanalyzed to determine which event produced the greatestBRB demand. Of the 20 synthetic earthquake records,LA20 generated the highest BRB demand in terms of max-imum brace displacement and cumulative ductility. Firststory compression dominated brace axial displacement timehistory response for LA20 is shown in Figure 9. This dis-placement history was simplified and scaled to develop arandom displacement history (Figure 10). In the simplifica-tion, large peak-to-peak displacements were retained andsmaller elastic cycles were neglected. Displacement values

were scaled such that the maximum compressive displace-ment corresponded to 1 percent story drift for the framegeometry of Figure 3. This was done for consistency withthe increasing amplitude protocol displacement demandand to scale the random displacement history demand from


Table 4 Three-Story BRBF Model Member Properties

StoryBF

Column

BF

Beam

Side Interior Mech. Perp. BF

(kip) (kN) (kip/in.) (kN/mm) (in. (mm (in. (mm

(1) (4) (5) (6) (7) (8) (9)

3 117 520 588 103

2 196 872 943 165 W12x96 W14x48 W14x48 W14x61 W14x74 W12x96 1,033 429,967,063 290 4,752,249

1 243 1081 1088 191

Non-BF Columns (Minor Axis)Brace Yield ForceHoriz. Brace

Stiffness

P y K h

(2) (3)

Z yI y

(11)(10)

Table 4. Three-Story BRBF Model Member Properties

Time (sec.)

Dis

plac

emen

t (in

)

0 5 10 15 20 25 30-2

-1.5

-1

-0.5

0

0.5

1

1.5

Fig. 9. First story BRB axial displacement time history for LA20.

Time (min.)

Dis

plac

emen

t (in

)

0 2 4 6 8 10 12-2

-1.5

-1

-0.5

0

0.5

1

1.5

Fig. 10. Simplified random displacement history imposed on specimen 50 DB-2.

the larger analytically modeled CYB to the smaller experi-mentally tested CYB. The random displacement historywas applied at the same 1.33 in./min (33.78 mm/min) dis-placement rate as the increasing amplitude displacementhistory. Multiple iterations of this random displacement his-tory were applied to specimen 50P-2. After each iteration,both load and displacement were returned to zero with anadditional small inelastic displacement and elastic unloading.

EXPERIMENTAL RESULTS

Parameters Used for Comparison

AISC/SEAOC Recommended Buckling-Restrained BraceFrame Provisions (AISC/SEAOC, 2001) specify that theratio of maximum compressive force to maximum tensileforce (β) shall not exceed 1.3. This criterion serves to limitpotential unbalanced forces and ensures reasonably sym-metric hysteretic behavior. BRB demand from the increas-ing amplitude displacement protocol defined in theAISC/SEAOC Provisions is based on nonlinear dynamic

time history analysis of buckling-restrained braced frame(BRBF) buildings (Sabelli, 2000). BRBs are required toachieve displacements corresponding to 1.5 ∆bm (mean ofSabelli analysis) and cumulative ductilities of 140 ∆by(mean plus one standard deviation of Sabelli analysis).These are believed to be conservative values and may berevised as more data becomes available (AISC/SEAOC,2001).

Test Observations

Results for all specimens are summarized in Table 5. Dis-placements reported in hysteresis figures are the CYByielding core axial displacement. Typically the majority ofcore displacement relative to the tube took place at the actu-ator end of the specimen. It is believed this was due to theresistance to tube movement provided by the small fric-tional force developed between the yielding core, confiningmaterial, and steel pipe.

Bolt slip was not observed, indicating adequate slip crit-ical connection design. Detailing of Class-A slip surface


Table 5 CYB Performance Summary

SpecimenCumulative

Ductility

Fracture

On Cycle

1st

Compressive

Degradation

On Cycle

(kip) (kN) (kip) (kN) (C/T) (in.) (mm) (in.) (mm) (kip-in.) (kN-mm) ( by )

(1) (4) (8) (9) (10)

125DBa-1 151.6 674.3 154.7 688.1 1.02 2.404 61.06 2.452 62.28 5,230 590,881 176 1 @ 2.0 bm 2 @ 1.5 bm

125DB-2 155.8 693.0 163.5 727.2 1.05 2.394 60.81 2.074 52.68 6,165 696,517 183 2 @ 2.0 bm 2 @ 1.5 bm

125DB-3 145.8 648.5 95.5 424.8 0.66 4.177 106.10 1.705 43.31 2,051 231,720 125c e

1 @ 0.5 bm

125DB-4 143.6 638.7 137.0 609.4 0.95 2.969 75.41 2.803 71.20 5,852 661,154 272 1 @ 3.0 bm 3 @ 0.5 bm

125DB-5 167.2 743.7 143.9 640.1 0.86 2.391 60.73 2.057 52.25 5,785 653,585 216 2 @ 2.0 bm 2 @ 1.5 bm

125Pb-1 131.9 586.7 131.1 583.1 0.99 1.269 32.23 1.038 26.37 1,525 172,293 83

c4 @ 1.0 bm 1 @ 0.5 bm

125P-2 158.6 705.5 169.6 754.4 1.07 2.204 55.98 1.689 42.90 4,955 559,812 220 1 @ 2.0 bm 3 @ 1.0 bm

125P-3 159.9 711.2 182.4 811.3 1.14 2.364 60.05 2.342 59.49 5,858 661,832 261 1 @ 2.0 bm 2 @ 1.5 bm

125P-4 166.2 739.3 257.6 1145.8 1.55c

2.408 61.16 2.278 57.86 7,637 862,822 280e f

125P-5 167.1 743.3 252.9 1124.9 1.51c

2.410 61.21 2.095 53.21 6,792 767,355 236e f

50DB-1 64.6 287.3 68.8 306.0 1.07 1.816 46.13 1.660 42.16 1,957 221,100 182 3 @ 1.5 bm 4 @ 1.0 bm

50DB-2 68.0 302.5 78.2 347.8 1.15 2.356 59.84 2.344 59.54 1,230 138,964 101c e

2 @ 1.5 bm

50P-1 67.0 298.0 73.3 326.0 1.09 1.804 45.82 1.715 43.56 1,639 185,173 195 2 @ 1.5 bm 2 @ 1.0 bm

50P-2 57.9 257.5 72.1 320.7d

0.718 18.24 1.223 31.06 1,475 166,660 180e

Iteration 3


cDoes not meet AISC / SEAOC Provisions


dUnequal tensile and compressive displacements

eLimit state other than fracture

fCompressive Degradation not observed

(6) (7)

Max.

Tensile

Force

T

(2) (3) (5)

Total Energy

Dissipated

Max.

Compressive

Displacement

Max.

Tensile

Displacement

Max.

Compressive

Force

C

Table 5. CYB Performance Summary

eliminated the expense of sand-blasted faying surfaces anddid not diminish CYB performance.

Yielding was distributed along the entire reduced sectionyielding core length for both the dogbone and perforatedconfigurations as evidenced by uniform flaking of millscale. Strain gages on the yielding core did not indicatebending (with the exception of 125DB-3) and showed bal-anced strains at instrumented locations up to the 3000microstrain range limitation of the gages. Confining tubestrain gages did not indicate significant bending.

The typical failure mechanism observed was fracture ofthe steel yielding core induced by increased tensile strainsdue to local high amplitude buckling at the actuator end ofthe specimen. This is an undesirable failure mechanism. Itis anticipated that increasing the length of unreduced crosssection within the confining tube would provide increasedbuckling resistance for this portion of the device. Thiswould provide a larger unreduced yielding core surface areato be in contact with the confining material thereby limitingbuckling and the associated bending induced tensile strains.This improved detail requires future experimental verification.

Confining Material Effects

CYB performance was determined to be highly dependenton the particle size of the confining material. 125DB spec-imens were tested using pea gravel, sand, 3/4 in. (19.05 mm)to #4 gravel, and 3/4 in. (19.05 mm) minus gravel.

Specimen 125DB-2 tested with pea gravel confiningmaterial provided reasonably stable and symmetric hys-teretic response. The load-displacement curve for this spec-imen is shown in Figure 11. During the last few cycles ofcompressive displacement local large-amplitude yieldingcore buckling took place within the confining tube near theactuator end of the specimen. The resulting compressive

degradation can be observed in the hysteretic response.Reduced tension capacity of the yielding core was alsoobserved during reloading in tension and straightening ofthe local large-amplitude buckling. The β value of 1.05 iswell within the suggested 1.3 limit and in line with a com-pressive overstrength of 1.1 typical of UBBs. A total of6,165 kip-in. (696 517 kN-mm) of energy was dissipated bythe device. The cumulative ductility of 183 ∆by exceededthe 140 ∆by requirement of the AISC/SEAOC Provisions.

Pea gravel confining material was also used for specimen50DB-1. Figure 12 shows reasonably stable and symmetricdissipation of 1,957 kip-in. (221 100 kN-mm) of energy.The capacity reduction observed in the last few cycles ofdisplacement was similar to that explained above for speci-men 125DB-2. The β value was 1.07 and a cumulative duc-tility of 182 ∆by was achieved. The smaller yield forcedevice dissipated proportionally less energy but stillachieved approximately the same cumulative ductility as125DB-2.

Sand confining material did not adequately prevent theyielding core (125DB-3) from translating through the con-fining material. As a result the core buckled in approxi-mately the fourth mode in the weak direction and secondmode in the strong direction. The load-displacement curve(Newell, 2003) showed buckling with significant pinchingof the hysteresis loops. Sand confining material for thisspecimen geometry does not provide sufficient confinementto enable stable and symmetric hysteretic damping.

Testing with 3/4 in. (19.05 mm) to #4 gravel resulted insignificant confining material crushing and considerablelocalized buckling at the ends of the reduced section ofspecimen 125DB-4. Compressive degradation wasobserved significantly earlier than with pea gravel or 3/4 in.(19.05 mm) minus gravel confining material (cycle 3 @ 0.5∆bm vs. cycle 2 @ 1.5 ∆bm). The 3/4 in. (19.05 mm) to #4


Displacement (in.)

Load

(kip

)

-3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3-200

-150

-100

-50

0

50

100

150

200

Theoretical StiffnessNominal Yield

Fig. 11. Specimen 125DB-2 hysteresis.

Displacement (in.)

Load

(kip

)

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5-100

-75

-50

-25

0

25

50

75

100


Fig. 12. Specimen 50DB-1 hysteresis.

gravel is not an optimal confining material for this speci-men geometry.

Specimen 125DB-5 tested with 3/4 in. (19.05 mm) minusgravel confining material performed similar to specimen125DB-2 confined with pea gravel. The larger aggregatelocks together preventing translation of particles, with finesfilling voids. No significant benefit was observed by usingthe 3/4 in. (19.05 mm) minus gravel. Pea gravel was used asthe confining material for the remaining tests, and the costsassociated with producing the 3/4 in. (19.05 mm) minusgravel blend were avoided.

Testing of different confining material indicated that par-ticle size and shape must be such that localized crushing ofthe confining material does not create a significant volumeloss, and that there is adequate particle interlock so that theyielding core cannot translate through the confining mate-rial.

Perforation Blocking Effects

Specimen 125P-1 was tested with perforations filled withspray foam to prevent the yielding core perforation endsfrom bearing on the pea gravel confining material. Desir-able structural performance was not achieved, with the legsof the first perforation at the actuator end buckling into thevoid space. Abrupt stiffening occurred when the buckledlegs came into contact with each other.

Following the poor performance of specimen 125P-1,different configurations of perforation blocking were inves-tigated to prevent buckling of perforation legs. Further,design factors of safety against buckling of legs should beincreased. Combinations where the complete width of thefirst two perforations at each end and partial width (voidspace width minus 1/2 in.) of the remaining perforationswere blocked with steel plate provided the best perform-

ance. Future testing may confirm that perforation blockingcould be completely avoided by detailing shorter perfora-tion leg lengths, while still achieving large ductility.

Reasonably stable and symmetric hysteretic behavior isshown in Figure 13, for specimen 125P-5. The first two per-forations at each end were completely blocked with theoriginal knockout from water jet cutting. Remaining perfo-rations were blocked using steel plate 2 in. (50.8 mm)shorter and 1/2 in. (12.7 mm) narrower than the perforationdimensions. The compressive elastic stiffness for thisblocked configuration was 845 kip/in. (148 kN/mm), whichwas 1.45 times greater than the compression stiffness withno perforation blocking. This accounts for the compressivestiffening observed in the hysteresis curve. The β value of1.51 is above the AISC/SEAOC 1.3 limit. Future detailingof shorter legs would eliminate the need for perforationblocking and the associated compressive stiffening. A totalof 6,792 kip-in. (696 517 kN-mm) of energy was dissipatedby the device. A cumulative ductility of 236 ∆by wasachieved before testing was suspended to prevent damageto the reaction system from the high compressive forces.

Specimen 50P-1 was tested with the first two perfora-tions at each end blocked with a steel plate 1 in. (25.4 mm)shorter and equal in width to the perforation dimension.Remaining perforations were blocked with steel plates 1 in.(25.4 mm) shorter and 1/2 in. (12.7 mm) narrower than theperforation dimension. The hysteresis curve (Figure 14)indicates reasonably stable and symmetric hysteretic damp-ing. Compressive stiffening (observed in specimen 125P-5)was eliminated by not blocking the full length of end perfo-rations. The weak direction of each perforation leg was inthe out-of-plane direction, and buckling was observed in theout-of-plane direction and thus not restrained by perforationblocking. This specimen dissipated 1,639 kip-in.


Displacement (in.)

Load

(kip

)

-3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3-300

-250

-200

-150

-100

-50

0

50

100

150

200


Fig. 13. Specimen 125P-5 hysteresis.

Displacement (in.)

Load

(kip

)

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5-100

-75

-50

-25

0

25

50

75

100



(185 173 kN-mm) of energy. The β value was 1.09 and acumulative ductility of 195 ∆by was achieved.

Decreasing Amplitude Displacement History

A decreasing amplitude displacement history was applied tospecimen 50DB-2. One cycle at 2.0 ∆bm (2 percent storydrift) was followed by two cycles at 1.5 ∆bm. Yielding corefracture was observed on the subsequent cycle at 1.0 ∆bm.The energy dissipated and cumulative ductility were 1,230kip-in. (138 964 kN-mm) and 101 ∆by, respectively. Thesevalues are less than those of specimen 50DB-1 subjected tothe increasing amplitude displacement protocol. However,for specimen 50DB-2 the largest single excursion displace-ment was 0.5 ∆bm larger. This indicates that device per-formance has some dependence on applied displacementhistory. This observation is unique to CYB devices due tolocal crushing of confining material and rearrangement ofparticles during cycle loading. The increasing amplitudedisplacement protocol does not adequately indicate per-formance capability of CYBs for large excursions due todamage accumulated at lower displacement amplitudes.The devices can sustain very large excursions whensequenced at the beginning of the record before local crush-ing of confining material has occurred.

Random Displacement History

Specimen 50P-2 was subjected to the random displacementhistory derived from nonlinear time-history analysis asdescribed previously. Seven complete iterations of the ran-dom displacement and an eighth iteration up to the point ofmaximum compressive displacement were applied. Load-ing was suspended at maximum compressive displacement

to examine the yielding core in that state. Buckling andcompressive stiffening was observed in the hysteresis curve(Figure 15). Based on visual observation after removal ofthe core plate, local buckling of the core against the confin-ing tube resulted in the post-buckling compressive stiffen-ing. Figure 16 presents each individual iteration of randomdisplacement history and shows minor progressive degra-dation in CYB performance. There was a gradual decreasein the energy dissipated per iteration (Table 6) due to pinch-ing of the hysteresis loops. Cumulative ductility values periteration however do not capture the performance degrada-tion because the same displacement amplitudes wereachieved, but at lower axial forces. Therefore, performancespecifications should include not only cumulative ductilityand tension/compression ratios, but also measures of per-


Table 6 Random Displacement History Iteration Comparison

IterationCumulative

Ductility

(kip) (kN) (kip) (kN) (C /T ) (in.) (mm) (in.) (mm) (kip-in.) (kN-mm) ( by )

(1) (4) (8)

1 56.4 250.8 65.1 289.4 1.15 0.718 18.24 1.176 29.87 230 26,039 24.0

2 53.8 239.3 72.1 320.9 1.34 0.719 18.26 1.186 30.12 223 25,186 24.6

3 56.9 253.1 70.0 311.5 1.23 0.724 18.39 1.185 30.10 211 23,891 24.3

4 57.9 257.7 65.5 291.3 1.13 0.726 18.44 1.188 30.18 196 22,134 24.3

5 57.6 256.1 63.0 280.3 1.09 0.727 18.47 1.183 30.05 186 20,990 24.4

6 57.2 254.3 62.0 275.9 1.09 0.727 18.47 1.186 30.12 179 20,233 24.5

7 55.8 248.0 58.4 259.7 1.05 0.692 17.58 1.149 29.18 159 18,019 22.8

8 54.3 241.4 58.4 259.6 1.08 0.698 17.73 1.132 28.75 90 10,167 11.5

Total 1474 166,659 180.4

Total Energy

Dissipated

(2) (3) (5) (6) (7)

Max. Tensile

Force

T

Max. Compressive

Force

C

Max. Tensile

Displacement

Max. Compressive

Displacement

Table 6. Random Displacement History Iteration Comparison

Displacement (in.)

Load

(kip

)

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5-100

-75

-50

-25

0

25

50

75

100



centage change in energy dissipation or secant stiffness onsubsequent cycles of similar amplitude to ensure that localbuckling behavior, possible with confining materials otherthan concrete, do not significantly degrade device perform-ance.

Experimental results for specimen 50P-2 were comparedwith a time-history response for a single CYB subjected tothe imposed random displacement history. Brace modelproperties were determined in the same manner as the threestory building analysis. When compared to actual CYB per-formance, equal compressive and tensile yield strengthsmore accurately reflected experimental results. An effi-ciency factor of 80 percent was applied to Young’s Modu-

lus to better represent CYB elastic stiffness. Also, a strainhardening modulus of 7.5 percent was observed to moreaccurately reflect CYB post-yield stiffness. Experimentaland analytical results are illustrated in Figure 17. Theenergy dissipated by specimen 50P-2 iteration 2 was 223kip-in. (25,186 kN-mm) while the analytical model dissi-pated 170 kip-in. (19,206 kN-mm). The analytical modelunderestimated the energy dissipation capacity of the CYB.

The response of the three-story building model wasassessed using the experimental CYB properties to deter-mine if the imposed random displacement history was areasonable representation of the model BRB demand.Analysis with experimental CYB properties resulted in sim-ilar cumulative brace displacement demand.


Displacement (in.)

Load

(kip

)

Iteration 1

-1.5 -1 -0.5 0 0.5-75

-50

-25

0

25

50

75

Displacement (in.)

Load

(kip

)

Iteration 2

-1.5 -1 -0.5 0 0.5 1 1.5-75

-50

-25

0

25

50

75

Displacement (in.)

Load

(kip

)

Iteration 3

-1.5 -1 -0.5 0 0.5-75

-50

-25

0

25

50

75

Displacement (in.)

Load

(kip

)

Iteration 4

-1.5 -1 -0.5 0 0.5 1 1.5-75

-50

-25

0

25

50

75

Displacement (in.)

Load

(kip

)

Iteration 5

-1.5 -1 -0.5 0 0.5-75

-50

-25

0

25

50

75

Displacement (in.)

Load

(kip

)

Iteration 6

-1.5 -1 -0.5 0 0.5 1 1.5-75

-50

-25

0

25

50

75

Displacement (in.)

Load

(kip

)

Iteration 7

-1.5 -1 -0.5 0 0.5-75

-50

-25

0

25

50

75

Displacement (in.)

Load

(kip

)

Iteration 8

-1.5 -1 -0.5 0 0.5 1 1.5-75

-50

-25

0

25

50

75

1 1.5

1 1.5

1 1.5

1 1.5

Fig. 16. Specimen 50P-2 hysteresis for each iteration of imposed random displacement history.

CONCLUSIONS

A new type of tension-compression yielding brace or buck-ling-restrained brace has been investigated and tested forseismic applications. The Confined Yielding Brace consistsof a steel yielding core element within a structural tubefilled with non-cohesive material. This non-cohesive mate-rial is placed under a normal confining force to providebuckling resistance of the core, enabling the device to yieldin compression without global buckling of the brace. Thetesting program examined the effects of different confiningmaterial, perforation blocking configurations, and randomdisplacement histories. Based on Confined Yielding Bracestest results, the following observations and conclusions arepresented:

1. A properly designed, detailed, and constructed CYBdevice exhibits reasonably stable and symmetric hys-teretic response under fully reversed cyclic loading.

2. Bolt slip was avoided with slip-critical bolted connec-tions, Class-A slip surfaces, and fully-tensioned A490high-strength structural bolts.

3. Confining material particle size and shape must be suchthat localized crushing of the confining material does notcreate a significant volume loss, while providing ade-quate particle interlock to limit yielding core translationthrough the confining material.

4. Gradual degradation on compressive cycles wasobserved when a CYB was subjected to multiple itera-tions of a random displacement history, although the per-formance as measured by cumulative ductility or energydissipation did not diminish significantly even after thesixth iteration.

5. Performance Specifications for CYBs should considerother quantitative measures to ensure reasonably stableand symmetric hysteretic response. Change in energydissipation or secant stiffness on subsequent cycles ofsimilar amplitude would provide an additional measureof device performance.

6. Nonlinear dynamic time history response calculatedusing experimentally determined CYB load-deformationproperties resulted in cumulative brace displacementdemand similar to that determined in development of therandom displacement protocol using brace propertiesbased on previous UBB testing.

7. The cross-sectional area and mechanical properties ofthe yielding core can be tailored to provide a device withthe desired strength, stiffness, and yield surface proper-ties. Use of the perforated configuration provides greaterflexibility in design.

8. The CYB can provide performance similar to other typesof buckling-restrained braces, and has the additionalbenefits of reduced cost, post-event inspection, designflexibility, reduced detailing, and can be designed andfabricated for relatively low-force applications.

The Confined Yielding Brace can provide a cost effectivepassive energy dissipation/buckling-restrained brace optionthat builds upon the strengths of the UBB. Desired struc-tural performance properties of the CYB can be achieved byvarying the cross-sectional area and mechanical propertiesof the steel core. Strength, stiffness, and yield surface prop-erties can be adjusted using conventional grades of steel anddifferent geometry of the steel core element, facilitatingperformance-based design objectives.

ACKNOWLEDGMENTS

This research was funded by the National Science Founda-tion (NSF) under Grant No. CMS-0099701 as part of theUS-Japan Cooperative Research in Urban Earthquake Dis-aster Mitigation Program. Professor K. Kasai of the TokyoInstitute of Technology is the Japanese counterpart and Dr.Peter Chang was the program manager. Additional fundingfrom the 2002 AISC/Klingelhofer Fellowship supportedthis research. Their support is gratefully acknowledged. Theopinions, findings, and conclusions are those of the authorsand do not necessarily reflect the views of NSF, AISC, orthe individuals acknowledged above.

REFERENCES

American Institute of Steel Construction (AISC) (1993),Load and Resistance Factor Design Specification forStructural Steel Buildings, Chicago, December 1.


Displacement (in.)

Load

(kip

)

-1.5 -1 -0.5 0 0.5 1 1.5-100

-75

-50

-25

0

25

50

75

100

PC-ANSRSpecimen 50P-2 (Iter. 2)

Fig. 17. Experimental and analytical force-deformation response for specimen 50P-2 during second iteration

of imposed random displacement history.

American Institute of Steel Construction / Structural Engi-neers Association of California (AISC/SEAOC) (2001),“Recommended Buckling-Restrained Braced FrameCode Provisions,” Chicago.

Applied Technology Council (ATC) (1992), “Guidelines forCyclic Seismic Testing of Components of Steel Struc-tures,” ATC-24, Redwood City, CA.

Aiken, I., Clark, P., Tajirian, F., Kasai, K., Kimura, I., andKo, E. (2000), “Unbonded Braces in the United States-Design Studies, Large-Scale Testing and the First Build-ing Application,” Proceedings of InternationalSymposium on Passive Control, pp. 203-217, TokyoInstitute of Technology, Tokyo, Japan.

Black, C., Makris, N., and Aiken, I. (2002), “ComponentTesting, Stability Analysis and Characterization of Buck-ling Restrained Braces,” Final Report to Nippon SteelCorporation, Tokyo, Japan.

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FEMA (2003), “NEHRP Recommended Provisions forNew Buildings and Other Structures,” FEMA 450, Wash-ington, D.C.

Higgins, C. and Newell, J. (2002), “Development of TwoNew Hysteretic Dampers,” Proceedings of the 7th U.S.National Conference on Earthquake Engineering,Boston, July.

Higgins, C. and Newell, J. (2001), “Development of Eco-nomical Hysteretic Dampers,” Proceedings of the Inter-national Symposium on Passive Control, Tokyo Instituteof Technology, Tokyo, Japan, December.

International Conference of Building Officials (ICBO)(1997), “Uniform Building Code,” Whittier, California.

Maison, B. (1992), “PC-ANSR A Computer Program forNonlinear Structural Analysis,” University of California,Berkeley, CA.

Merritt, S., Uang, C.M., and Benzoni, G. (2003a), “Sub-assemblage Testing of Corebrace Buckling-RestrainedBraces,” University of California, San Diego, Report No.TR-2003/01, La Jolla, CA.

Merritt, S., Uang, C.M., and Benzoni, G. (2003b), “Sub-assemblage Testing of Star Seismic Buckling-RestrainedBraces,” University of California, San Diego, Report No.TR-2003/04, La Jolla, CA.

Merritt, S., Uang, C.M., and Benzoni, G. (2003c), “Uniax-ial Testing of Associated Buckling-Restrained Braces,”University of California, San Diego, Report No. TR-2003/05, La Jolla, CA.

Newell, J. (2003), “Steel Confined Yielding Damper forEarthquake Resistant Design,” M.S. Thesis, Oregon StateUniversity, Corvallis, OR.

Research Council on Structural Connections (RCSC)(1994), Specification for Structural Joints Using ASTMA325 or A490 Bolts, Chicago.

Sabelli, R. (2000), “Research of Improving the Design andAnalysis of Earthquake-Resistant Steel-Braced Frames,”2000 NEHRP Professional Fellowship Report, EERI,Oakland, CA.

Tremblay, R., Degrange, G., and Blouin, J. (1999), “SeismicRehabilitation of a Four-Storey Building with a StiffenedBracing System,” Proceedings of 8th Canadian Confer-ence on Earthquake Engineering, Vancouver, B.C.

Watanabe, A. (1992), “Development of Composite Bracewith a Large Ductility,” U.S.-Japan Workshop on Com-posite and Hybrid Structures, San Francisco.

Watanabe, A., Hitomi, Y., Saeki, E., Wada, A., and Fuji-moto, M. (1988), “Properties of Brace Encased in Buck-ling-Restraining Concrete and Steel Tube,” Proceedingsof 9th World Conference on Earthquake Engineering,Paper No. 6-7-4., Vol. IV, pp. 719-724, Tokyo-Kyoto, Japan.

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higgins - confined steel brace for earthquake resistant design

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